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Alternative Expressions for the Power of a Point

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Explanations 1

In the diagram, OOO is the center of the circle, which has (let's say) radius RRR. Out of the 3 ways to represent the power above, the third way (PA⋅PBPA \cdot PBPA⋅PB) is the l…
By Yang Liu

Problems 3

DEBDEBDEB is a chord of a circle such that DE=3DE=3DE=3 and EB=5EB=5EB=5. Let OOO be the center of the circle. Join OEOEOE and extend OEOEOE to cut the circle at CCC. Given EC=1…
Two circles have radius 5 and 26. The smaller circle passes through center of the larger one. What is the difference between the lengths of the longest and shortest chords of th…
In a circle, chords ABABAB and CDCDCD intersect at RRR. If AR:BR=1:4AR:BR = 1:4AR:BR=1:4 and CR:DR=4:9CR:DR = 4:9CR:DR=4:9, find the ratio AB:CDAB:CDAB:CD.